No, bran is only part of the grain. Whole grains are made up of the bran (the outside coating, just under the hard shell that is removed), the germ (at the center of the grain, and source of vitamin E and other vitamins), and the endosperm (the bulk of the grain, which sits between the bran and the germ, and what is left in white flour, for example: think of a grain like a flame---the germ is that center brightest part, and endosperm the next layer, and the bran the outside border).
Oat bran is high in fiber particularly. Adding it to oatmeal isn't a bad idea.